A frog is climbing a greasy pole. The frog can climb 2

BTGmoderatorLU wrote:Source: Veritas Prep

A frog is climbing a greasy pole. The frog can climb 2 centimeters every half-hour and it takes a break to rest for half an hour after every 2 hours, during which it slips by 1 centimeter. How much time it will take to climb a 28-centimeter pole?

A. 7.5 hours
B. 8.5 hours
C. 9.25 hours
D. 9.75 hours
E. 10 hours

Let's solve this by making table

Time elapsed | height
1 hours | 4 cm
2 hours | 8 cm
REST (slide)
2.5 hours | 7 cm
3.5 hours | 11 cm
4.5 hours | 15 cm
REST (slide)
5 hours | 14 cm
6 hours | 18 cm
7 hours | 22 cm
REST (slide)
7.5 hours | 21 cm
8.5 hours | 25 cm
9.5 hours | 29 cm
Oops - we want too far.
We can see that the frog reaches a height of 28 cm BETWEEN 8.5 hours and 9.5 hours.
So, the correct answer must be C

Cheers,
Brent

BTGmoderatorLU wrote:Source: Veritas Prep

A frog is climbing a greasy pole. The frog can climb 2 centimeters every half-hour and it takes a break to rest for half an hour after every 2 hours, during which it slips by 1 centimeter. How much time it will take to climb a 28-centimeter pole?

A. 7.5 hours
B. 8.5 hours
C. 9.25 hours
D. 9.75 hours
E. 10 hours

The OA is C.

In 2.5 hours, the frog can climb a total of 8 centimeters but will slip back 1 centimeter; thus, it will have covered a distance of 7 centimeters. We need to be careful not to just conclude that it will take 2.5 x 4 = 10 hours, because once the frog reaches the top, it will not rest and slip back again. Instead, we proceed as follows:

In 7.5 hours, the frog will be 21 centimeters high.

In 8 hours, the frog will be at 23 centimeters.

In 8.5 hours, the frog will be at 25 centimeters.

In 9 hours, the frog will be at 27 centimeters.

Since it takes 0.5 hours to climb 2 centimeters, it will take 0.25 hours to climb the final centimeter, and thus the frog will be on the top of the 28-centimeter pole in 9 + 0.25 = 9.25 hours.

Answer: C